Old and New Examples of Scale Functions for Spectrally Negative Levy Processes

By Friedrich Hubalek, E. Kyprianou. 2007

120 citations recorded by the source corpus.

We give a review of the state of the art with regard to the theory of scale functions for spectrally negative Levy processes. From this we introduce a general method for generating new families of scale functions. Using this method we introduce a new family of scale functions belonging to the Gaussian Tempered Stable Convolution (GTSC) class. We give particular emphasis to special cases as well as cross-referencing their analytical behaviour against known general considerations.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/5c44bffe7bbb648148dac7dffd81f4f0fba7125e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

In Management Science and Operations Research

Citations in the corpus

General tax Structures and the Lévy Insurance Risk Model (2009, unknown): “See, for example, [8], [9], [15], and [17].”
An Optimal Dividends Problem with a Terminal Value for Spectrally Negative Lévy Processes with a Completely Monotone Jump Density (2009, unknown): “We refer to the papers [13, 17, 19] for an updated account on explicit examples of scale functions and their properties.”
The Theory of Scale Functions for Spectrally Negative Lévy Processes (2011, methodology): “See Caballero et al. [26] and Kyprianou and Pardo [67] for further computations in this spirit and Lambert [73] for further applications in population biology.”
An optimal dividends problem with transaction costs for spectrally negative Lévy processes (2009, unknown): “We refer to the papers [12, 17, 18] for an updated account on explicit examples of scale functions and their properties.”
Smoothness of scale functions for spectrally negative Lévy processes (2009, unknown): “For example, [8] formalise several facts which are implicit in the Wiener–Hopf factorisation.”
OCCUPATION TIMES OF SPECTRALLY NEGATIVE LÉVY PROCESSES WITH APPLICATIONS (2010, unknown): “Further information, examples, and numerical techniques related to the computation of scale functions can be found in [4,9,13,16,21].”
An Insurance Risk Model with Parisian Implementation Delays (2013, unknown): “As will be shown, all our results are expressed in terms of scale functions for which many explicit examples are known; see, e.g., Hubalek and Kyprianou (2010), Kyprianou and Rivero (2008).”
A note on scale functions and the time value of ruin for Levy insurance risk processes (2010, unknown): “It was shown in Hubalek and Kyprianou (2008) that the process X has no Gaussian component, has paths of unbounded variation, and its Levy measure is given by”